1. SADC Course in Statistics A Life Table Discussion Topic (Session 14)

2. To put your footer here go to View > Header and Footer 2 Learning Objectives – this session At the end of this session, you will be able to explain some further summaries of survivorship data in Life Tables discuss some issues relating to the application of Life Table methodology think constructively about approaches to new practical applications of Life Table ideas

3. To put your footer here go to View > Header and Footer 3 Introduction Wikipedia is a public-domain web resource with articles contributed voluntarily by the readership. In August 2007 search for Life Table produced definitions given below & an interesting diagram, reproduced below. The summary description of the diagram was incomprehensible, so this session focuses on studying the diagram, & figuring out how to reproduce and explain what it shows. See http://en.wikipedia.org/wiki/Life_table

4. To put your footer here go to View > Header and Footer 4 New LT summaries As well as q x, p x = 1-q x, l x and d x the article introduces t p x : the probability that someone aged exactly x will survive for t more years, & t|k q x : the probability that someone aged exactly x will survive for t more years, then die within the next k years. Why would someone want to know this?

5. To put your footer here go to View > Header and Footer 5 Insurers interests If a man of working age x takes out an annuity-based pension from an insurer, the insurance deal might be that:- he pays premiums for t more years till he reaches retirement age, if he survives longer the insurer pays him an annual sum for the rest of his life, or if he dies before retirement his premiums are lost So insurer would want to estimate t|k q x

6. To put your footer here go to View > Header and Footer 6 The Wikipedia illustration FOR CLASSROOM DISCUSSION BY YOU, facilitated by your trainer:- The illustration shown in the web reference is the following diagram of various values of t p x with x-values being the age scale (x- axis) and each curve showing a different minimum survival time t in a different colour. The data depicted draw on a 2003 Life Table for the total population of the US http://upload.wikimedia.org/wikipedia/commons/b/be/Excerpt_from_CDC_2003_Table_1.png

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8. 8 The added lines shown on the diagram read off a value of about 0.87 corresponding to x = 40. What is your interpretation of this point? Q.1

9. To put your footer here go to View > Header and Footer 9 The added lines shown on the diagram read off a value of about 0.89 corresponding to x = 50. What is your interpretation of this point? Q.2

10. To put your footer here go to View > Header and Footer 10 Q.3 Give your explanation as to why the second value above (0.89) is higher than the first (0.87). Discuss! Note that the values given above are roughly read off from the graphs shown. They have not been computed.

11. To put your footer here go to View > Header and Footer 11 The added line shown on the diagram reads off 5 values corresponding to x = 60. What is your interpretation of this set of values? Q.4

12. To put your footer here go to View > Header and Footer 12 The added line shown on the diagram reads off 5 values corresponding to t p x = 0.5. What is your interpretation of this set of values? Q.5

13. To put your footer here go to View > Header and Footer 13 Q.6 In terms of LT algebra can you discuss, agree and write down the formula for:- t p x : the probability that someone aged exactly x will survive for t more years, & Q.7 In terms of LT algebra can you discuss, agree and write down the formula for:- t|k q x : the probability that someone aged exactly x will survive for t more years, then die within the next k years?

14. To put your footer here go to View > Header and Footer 14 Q.8 Why would it be very difficult to produce a diagram like the above? for t|k q x ? Q.9 An insurance company wants a set of illustrations of t|k q x in order to familiarise its annuity sales staff with the way its annuity policies work. Discuss what graphs you think it might be worth producing, and how you would explain them.

15. To put your footer here go to View > Header and Footer 15 Some practical work follows …